Feature-based Time Series Forecasting

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# Feature-based Time Series Forecasting
### Thiyanga S. Talagala
### Forecasting for Social Good (F4SG): Democratising Forecasting

---

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  top: 50%;
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  transform: translate(-50%, -50%);
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## Road map

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background-image: url(img/jhu.png)
background-size: contain

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background-image: url(img/jhu.png)
background-position: 50% 60%1

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Let's visualize the coronavirus pandemic!

---

background-image: url(img/coronavirus.png)
background-size: 90px
background-position: 100% 6%

# Data: coronavirus package

```r
install.packages("coronavirus")
# devtools::install_github("RamiKrispin/coronavirus")
```

```r
library(coronavirus)
head(coronavirus, 8)
```

```
        date province             country       lat      long      type cases
1 2020-01-22                  Afghanistan  33.93911  67.70995 confirmed     0
2 2020-01-22                      Albania  41.15330  20.16830 confirmed     0
3 2020-01-22                      Algeria  28.03390   1.65960 confirmed     0
4 2020-01-22                      Andorra  42.50630   1.52180 confirmed     0
5 2020-01-22                       Angola -11.20270  17.87390 confirmed     0
6 2020-01-22          Antigua and Barbuda  17.06080 -61.79640 confirmed     0
7 2020-01-22                    Argentina -38.41610 -63.61670 confirmed     0
8 2020-01-22                      Armenia  40.06910  45.03820 confirmed     0
```

---

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104 country: Afghanistan","date: 2020-10-27 cases: 95 country: Afghanistan","date: 2020-10-28 cases: 113 country: Afghanistan","date: 2020-10-29 cases: 123 country: Afghanistan","date: 2020-10-30 cases: 66 country: Afghanistan","date: 2020-10-31 cases: 91 country: Afghanistan","date: 2020-11-01 cases: 76 country: Afghanistan","date: 2020-11-02 cases: 132 country: Afghanistan","date: 2020-11-03 cases: 95 country: Afghanistan","date: 2020-11-04 cases: 86 country: Afghanistan","date: 2020-11-05 cases: 121 country: Afghanistan","date: 2020-11-06 cases: 40 country: Afghanistan","date: 2020-11-07 cases: 58 country: Afghanistan","date: 2020-11-08 cases: 126 country: Afghanistan","date: 2020-11-09 cases: 138 country: Afghanistan","date: 2020-11-10 cases: 166 country: Afghanistan","date: 2020-11-11 cases: 146 country: Afghanistan","date: 2020-11-12 cases: 186 country: Afghanistan","date: 2020-11-13 cases: 174 country: Afghanistan","date: 2020-11-14 cases: 66 country: Afghanistan","date: 2020-11-15 cases: 205 country: Afghanistan","date: 2020-11-16 cases: 228 country: Afghanistan","date: 2020-11-17 cases: 213 country: Afghanistan","date: 2020-11-18 cases: 243 country: Afghanistan","date: 2020-11-19 cases: 253 country: Afghanistan","date: 2020-11-20 cases: 186 country: Afghanistan","date: 2020-11-21 cases: 140 country: Afghanistan","date: 2020-11-22 cases: 203 country: Afghanistan","date: 2020-11-23 cases: 282 country: Afghanistan","date: 2020-11-24 cases: 186 country: Afghanistan","date: 2020-11-25 cases: 210 country: Afghanistan","date: 2020-11-26 cases: 216 country: Afghanistan","date: 2020-11-27 cases: 123 country: Afghanistan","date: 2020-11-28 cases: 121 country: Afghanistan","date: 2020-11-29 cases: 272 country: Afghanistan","date: 2020-11-30 cases: 158 country: Afghanistan","date: 2020-12-01 cases: 242 country: Afghanistan","date: 2020-12-02 cases: 202 country: Afghanistan","date: 2020-12-03 cases: 119 country: Afghanistan","date: 2020-12-04 cases: 0 country: 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2020-09-04 cases: 75 country: Cabo Verde","date: 2020-09-05 cases: 75 country: Cabo Verde","date: 2020-09-06 cases: 55 country: Cabo Verde","date: 2020-09-07 cases: 28 country: Cabo Verde","date: 2020-09-08 cases: 42 country: Cabo Verde","date: 2020-09-09 cases: 73 country: Cabo Verde","date: 2020-09-10 cases: 84 country: Cabo Verde","date: 2020-09-11 cases: 94 country: Cabo Verde","date: 2020-09-12 cases: 60 country: Cabo Verde","date: 2020-09-13 cases: 102 country: Cabo Verde","date: 2020-09-14 cases: 26 country: Cabo Verde","date: 2020-09-15 cases: 65 country: Cabo Verde","date: 2020-09-16 cases: 74 country: Cabo Verde","date: 2020-09-17 cases: 85 country: Cabo Verde","date: 2020-09-18 cases: 78 country: Cabo Verde","date: 2020-09-19 cases: 45 country: Cabo Verde","date: 2020-09-20 cases: 71 country: Cabo Verde","date: 2020-09-21 cases: 24 country: Cabo Verde","date: 2020-09-22 cases: 56 country: Cabo Verde","date: 2020-09-23 cases: 75 country: Cabo Verde","date: 2020-09-24 cases: 67 country: Cabo Verde","date: 2020-09-25 cases: 149 country: Cabo Verde","date: 2020-09-26 cases: 73 country: Cabo Verde","date: 2020-09-27 cases: 70 country: Cabo Verde","date: 2020-09-28 cases: 46 country: Cabo Verde","date: 2020-09-29 cases: 83 country: Cabo Verde","date: 2020-09-30 cases: 124 country: Cabo Verde","date: 2020-10-01 cases: 102 country: Cabo Verde","date: 2020-10-02 cases: 79 country: Cabo Verde","date: 2020-10-03 cases: 91 country: Cabo Verde","date: 2020-10-04 cases: 64 country: Cabo Verde","date: 2020-10-05 cases: 73 country: Cabo Verde","date: 2020-10-06 cases: 85 country: Cabo Verde","date: 2020-10-07 cases: 106 country: Cabo Verde","date: 2020-10-08 cases: 93 country: Cabo Verde","date: 2020-10-09 cases: 92 country: Cabo Verde","date: 2020-10-10 cases: 104 country: Cabo Verde","date: 2020-10-11 cases: 159 country: Cabo Verde","date: 2020-10-12 cases: 83 country: Cabo Verde","date: 2020-10-13 cases: 99 country: Cabo Verde","date: 2020-10-14 cases: 117 country: 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2020-11-24 cases: 98 country: Cabo Verde","date: 2020-11-25 cases: 126 country: Cabo Verde","date: 2020-11-26 cases: 44 country: Cabo Verde","date: 2020-11-27 cases: 56 country: Cabo Verde","date: 2020-11-28 cases: 74 country: Cabo Verde","date: 2020-11-29 cases: 47 country: Cabo Verde","date: 2020-11-30 cases: 14 country: Cabo Verde","date: 2020-12-01 cases: 55 country: Cabo Verde","date: 2020-12-02 cases: 51 country: Cabo Verde","date: 2020-12-03 cases: 71 country: Cabo Verde","date: 2020-12-04 cases: 58 country: Cabo Verde","date: 2020-12-05 cases: 40 country: Cabo Verde","date: 2020-12-06 cases: 27 country: Cabo Verde","date: 2020-12-07 cases: 35 country: Cabo Verde","date: 2020-12-08 cases: 20 country: Cabo Verde","date: 2020-12-09 cases: 74 country: Cabo Verde","date: 2020-12-10 cases: 11 country: Cabo Verde","date: 2020-12-11 cases: 59 country: Cabo Verde","date: 2020-12-12 cases: 40 country: Cabo Verde","date: 2020-12-13 cases: 55 country: Cabo Verde","date: 2020-12-14 cases: 4 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53 country: Cabo Verde","date: 2021-02-14 cases: 41 country: Cabo Verde","date: 2021-02-15 cases: 20 country: Cabo Verde","date: 2021-02-16 cases: 24 country: Cabo Verde","date: 2021-02-17 cases: 63 country: Cabo Verde","date: 2021-02-18 cases: 37 country: Cabo Verde","date: 2021-02-19 cases: 63 country: Cabo Verde","date: 2021-02-20 cases: 51 country: Cabo Verde","date: 2021-02-21 cases: 49 country: Cabo Verde","date: 2021-02-22 cases: 24 country: Cabo Verde","date: 2021-02-23 cases: 17 country: Cabo Verde","date: 2021-02-24 cases: 72 country: Cabo Verde","date: 2021-02-25 cases: 40 country: Cabo Verde","date: 2021-02-26 cases: 52 country: Cabo Verde","date: 2021-02-27 cases: 71 country: Cabo Verde","date: 2021-02-28 cases: 76 country: Cabo Verde","date: 2021-03-01 cases: 32 country: Cabo Verde","date: 2021-03-02 cases: 51 country: Cabo Verde","date: 2021-03-03 cases: 75 country: Cabo Verde","date: 2021-03-04 cases: 63 country: Cabo Verde","date: 2021-03-05 cases: 62 country: Cabo 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Korea, South","date: 2020-10-02 cases: 75 country: Korea, South","date: 2020-10-03 cases: 64 country: Korea, South","date: 2020-10-04 cases: 73 country: Korea, South","date: 2020-10-05 cases: 75 country: Korea, South","date: 2020-10-06 cases: 114 country: Korea, South","date: 2020-10-07 cases: 69 country: Korea, South","date: 2020-10-08 cases: 54 country: Korea, South","date: 2020-10-09 cases: 72 country: Korea, South","date: 2020-10-10 cases: 58 country: Korea, South","date: 2020-10-11 cases: 97 country: Korea, South","date: 2020-10-12 cases: 102 country: Korea, South","date: 2020-10-13 cases: 84 country: Korea, South","date: 2020-10-14 cases: 99 country: Korea, South","date: 2020-10-15 cases: 47 country: Korea, South","date: 2020-10-16 cases: 73 country: Korea, South","date: 2020-10-17 cases: 91 country: Korea, South","date: 2020-10-18 cases: 76 country: Korea, South","date: 2020-10-19 cases: 58 country: Korea, South","date: 2020-10-20 cases: 91 country: Korea, South","date: 2020-10-21 cases: 119 country: Korea, South","date: 2020-10-22 cases: 155 country: Korea, South","date: 2020-10-23 cases: 77 country: Korea, South","date: 2020-10-24 cases: 61 country: Korea, South","date: 2020-10-25 cases: 119 country: Korea, South","date: 2020-10-26 cases: 88 country: Korea, South","date: 2020-10-27 cases: 103 country: Korea, South","date: 2020-10-28 cases: 125 country: Korea, South","date: 2020-10-29 cases: 114 country: Korea, South","date: 2020-10-30 cases: 126 country: Korea, South","date: 2020-10-31 cases: 124 country: Korea, South","date: 2020-11-01 cases: 97 country: Korea, South","date: 2020-11-02 cases: 75 country: Korea, South","date: 2020-11-03 cases: 118 country: Korea, South","date: 2020-11-04 cases: 125 country: Korea, South","date: 2020-11-05 cases: 145 country: Korea, South","date: 2020-11-06 cases: 89 country: Korea, South","date: 2020-11-07 cases: 143 country: Korea, South","date: 2020-11-08 cases: 126 country: Korea, South","date: 2020-11-09 cases: 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2020-11-01 cases: 0 country: Kyrgyzstan","date: 2020-11-02 cases: 1001 country: Kyrgyzstan","date: 2020-11-03 cases: 895 country: Kyrgyzstan","date: 2020-11-04 cases: 535 country: Kyrgyzstan","date: 2020-11-05 cases: 0 country: Kyrgyzstan","date: 2020-11-06 cases: 439 country: Kyrgyzstan","date: 2020-11-07 cases: 556 country: Kyrgyzstan","date: 2020-11-08 cases: 515 country: Kyrgyzstan","date: 2020-11-09 cases: 571 country: Kyrgyzstan","date: 2020-11-10 cases: 970 country: Kyrgyzstan","date: 2020-11-11 cases: 0 country: Kyrgyzstan","date: 2020-11-12 cases: 527 country: Kyrgyzstan","date: 2020-11-13 cases: 567 country: Kyrgyzstan","date: 2020-11-14 cases: 499 country: Kyrgyzstan","date: 2020-11-15 cases: 1030 country: Kyrgyzstan","date: 2020-11-16 cases: 0 country: Kyrgyzstan","date: 2020-11-17 cases: 486 country: Kyrgyzstan","date: 2020-11-18 cases: 425 country: Kyrgyzstan","date: 2020-11-19 cases: 422 country: Kyrgyzstan","date: 2020-11-20 cases: 386 country: Kyrgyzstan","date: 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class: center, middle

# What problems do you see in the plot?

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background-image: url(img/tukey.jpeg)
background-size: 200px
background-position: 100% 6%

# Time series features

- **Cognostics**: **Co**mputer-aided dia**gnostics** (John W. Tukey, 1985)

- Characteristics of time series

- Summary measures of time series

**Basic Principle**

- Transform a given time series `\(y=\{y_1, y_2, \cdots, y_n\}\)` into a feature vector `\(F = (f_1(y), f_2(y), \cdots, f_p(y))'\)`.

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## Examples of time series features

.pull-left[

- strength of trend

- strength of seasonality

- lag-1 autocorrelation

- spectral entropy

- proportion of zeros

]

.pull-right[

]